Equation 3.4 as it appears in the main text is incorrect. The correct equation is:
(C3.4)
\begin{align} \left (\frac {\partial \mathcal{P}}{\partial t} - \frac {\partial \boldsymbol{u}^{\infty }}{\partial t} \boldsymbol{\cdot }\boldsymbol{\nabla} _{\boldsymbol{v'}} \mathcal{P}\right ) + \left (\boldsymbol{u}^{\infty } + \boldsymbol{v'}\right ) \boldsymbol{\cdot }\left (\boldsymbol{\nabla} _{\boldsymbol{x}} \mathcal{P} - \boldsymbol{\nabla} _{\boldsymbol{x}} \boldsymbol{u}^{\infty } \boldsymbol{\cdot }\boldsymbol{\nabla} _{\boldsymbol{v'}} \mathcal{P}\right ) + \frac {\boldsymbol{F}^{\textit{ext}}}{m} \boldsymbol{\cdot }\boldsymbol{\nabla} _{\boldsymbol{v'}} \mathcal{P} \nonumber \\ = \boldsymbol{\nabla} _{\boldsymbol{v'}} \boldsymbol{\cdot } \left\{\left [f \, \boldsymbol{S}(\boldsymbol{v'})\right ] \, \mathcal{P} + D \, \boldsymbol{\nabla} _{\boldsymbol{v'}} \mathcal{P} \right\}. \end{align}
\begin{align} \left (\frac {\partial \mathcal{P}}{\partial t} - \frac {\partial \boldsymbol{u}^{\infty }}{\partial t} \boldsymbol{\cdot }\boldsymbol{\nabla} _{\boldsymbol{v'}} \mathcal{P}\right ) + \left (\boldsymbol{u}^{\infty } + \boldsymbol{v'}\right ) \boldsymbol{\cdot }\left (\boldsymbol{\nabla} _{\boldsymbol{x}} \mathcal{P} - \boldsymbol{\nabla} _{\boldsymbol{x}} \boldsymbol{u}^{\infty } \boldsymbol{\cdot }\boldsymbol{\nabla} _{\boldsymbol{v'}} \mathcal{P}\right ) + \frac {\boldsymbol{F}^{\textit{ext}}}{m} \boldsymbol{\cdot }\boldsymbol{\nabla} _{\boldsymbol{v'}} \mathcal{P} \nonumber \\ = \boldsymbol{\nabla} _{\boldsymbol{v'}} \boldsymbol{\cdot } \left\{\left [f \, \boldsymbol{S}(\boldsymbol{v'})\right ] \, \mathcal{P} + D \, \boldsymbol{\nabla} _{\boldsymbol{v'}} \mathcal{P} \right\}. \end{align}
(The letter C preceding the equation number denotes the corrected version.)
The analysis that follows equation 3.4 in the paper was performed using the correct equation (as it appears here), and hence remains unaffected.
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